Euler-Lagrange equations for variable-growth total variation

2025/04/18 by Górny, Wojciech, Łasica, Michał, Matsoukas, Alexandros · 3 citations
#35J20 #35J60 (Primary) 35J92 #35J75 #49J52 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.13559

Abstract

We consider a class of integral functionals with Musielak-Orlicz type variable growth, possibly linear in some regions of the domain. This includes p(x) power-type integrands with p(x)≥ 1 as well as double-phase p - q integrands with p=1. The main goal of this paper is to identify the L²-subdifferential of the functional, including a local characterisation in terms of a variant of the Anzellotti product defined through the Young's inequality. As an application, we obtain the Euler-Lagrange equation for the variant of the Rudin-Osher-Fatemi image denoising problem with variable growth regularising term.

Cited by

• Adaptive double-phase Rudin--Osher--Fatemi denoising model
• Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems
• On the solutions of a double-phase Dirichlet problem involving the 1-Laplacian

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